The generator matrix

 1  0  1  1  1  1  1  1  0  1 2X^2  1  1  1  1 2X  1 2X^2+X  1  1  1 2X^2+X  1  1 X^2+2X  1  1  1 2X^2+2X  1  1  1  1  X  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+2X  1 2X^2+X  X  1  1  1  1  1  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2 2X^2+2X+1 2X  1 2X^2+X+1  1 2X^2+2 2X+2 X+1 2X^2  1 2X+2  1  1 X^2+2X 2X+1  1 2X^2+2X+2  0  1 X+2 2X^2+1 2X^2+X+2  1 2X^2+X 2X^2+2X+1 2X+1  X  1  0 X^2+2 X+1 X^2+2X 2X^2+1  1 X^2+X+1 2X^2+2  X 2X^2+1 X^2+X+1 X^2+2 2X^2+2X+1 2X^2+2 X^2  0 2X+2 X^2+2X X^2+2X 2X^2+X X+1  1 2X^2+2X X+2 X+1 X+2  1 X+2  X 2X+2 X^2+X+2 2X^2+1 X+1 2X^2+2X+2 X^2+2X+1 2X^2+2X+2 2X^2+1  0  1 2X^2+X+2  1 2X^2+2  1  1 2X X^2 2X+1 2X+1 X^2+2X+1 2X X^2+X  X
 0  0 2X  0 2X^2 2X^2 X^2  0 X^2+2X 2X^2+X 2X^2+X 2X^2+X 2X^2+2X X^2+2X X^2+X X^2  0  0 X^2+X 2X^2+2X X^2+X 2X 2X^2+X X^2 2X X^2+X X^2 2X^2+2X X^2+X X^2+2X 2X 2X^2+X X^2+X 2X^2+X X^2+2X 2X 2X^2 2X^2+X 2X X^2 2X^2+2X X^2 2X^2+2X  0 2X^2+X 2X^2+X  0 2X^2+2X  X X^2+2X 2X X^2+X 2X^2 2X^2 X^2 X^2+2X 2X^2 X^2+2X 2X^2+2X  0 2X^2+2X  X 2X^2+2X X^2+2X 2X^2 X^2+X X^2+2X X^2 X^2 2X^2+X X^2+2X  0 2X^2+X X^2 2X^2+X 2X 2X  0  X 2X^2+2X 2X^2+X 2X^2 X^2+X X^2+X  0  X
 0  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 X^2  0  0 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0  0 X^2 X^2 2X^2 X^2  0  0  0  0 2X^2  0  0 X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2  0 X^2 X^2  0 X^2 2X^2 2X^2  0 X^2 X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+288x^164+506x^165+762x^166+1266x^167+1540x^168+1374x^169+1794x^170+1796x^171+1662x^172+2004x^173+1366x^174+1392x^175+1332x^176+934x^177+522x^178+468x^179+290x^180+78x^181+96x^182+58x^183+18x^184+24x^185+34x^186+12x^187+6x^188+8x^189+6x^191+8x^192+6x^193+6x^194+12x^195+6x^199+6x^201+2x^216

The gray image is a linear code over GF(3) with n=774, k=9 and d=492.
This code was found by Heurico 1.16 in 1.95 seconds.